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Ivahew [28]
2 years ago
15

Find the area of the triangle. Round to the nearest tenth.

Mathematics
1 answer:
Fiesta28 [93]2 years ago
5 0

Answer: 130

Step-by-step explanation:

Find the height of the triangle by using the pythagorean theorem

So the height is sqrt(100 - 25) = 5sqrt(3)

The area of the triangle is 30 * 5sqrt(3) / 2 = 75sqrt(3) = 129.9 = 130

You might be interested in
Divide. Give the exact answer, written as a decimal.
anygoal [31]

Answer:

11.9440

Step-by-step explanation:

long division

5 0
3 years ago
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A bank offers a savings account that currently pays 2% interest per year compounded monthly. The amount of money in the account
LekaFEV [45]
The appropriate choice is ...
.. <span>A. The initial amount in the account does not change because it is a factor that is independent of both the interest rate and t.

_____
In general, each of the variables in a formula is independent of the others. (Occasionally, you'll see a formula where that is not true, but then the "variable" will likely be indicated as a function of those things it is dependent upon.)</span>
6 0
3 years ago
A)A cuboid with a square x cm and height 2xcm². Given total surface area of the cuboid is 129.6cm² and x increased at 0.01cms-¹.
Nutka1998 [239]

Answer: (given assumed typo corrections)


(V ∘ X)'(t) = 0.06(0.01t+3.6)^2 cm^3/sec.


The rate of change of the volume of the cuboid in change of volume per change in seconds, after t seconds. Not a constant, for good reason.



Part B) y'(x+Δx/2)×Δx gives exactly the same as y(x+Δx)-y(x), 0.3808, since y is quadratic in x so y' is linear in x.


Step-by-step explanation:

This problem has typos. Assuming:

Cuboid has square [base with side] X cm and height 2X cm [not cm^2]. Total surface area of cuboid is 129.6 cm^2, and X [is] increas[ing] at rate 0.01 cm/sec.


129.6 cm^2 = 2(base cm^2) + 4(side cm^2)

= 2(X cm)^2 + 4(X cm)(2X cm)

= (2X^2 + 8X^2)cm^2

= 10X^2 cm^2

X^2 cm^2 = 129.6/10 = 12.96 cm^2

X cm = √12.96 cm = 3.6 cm


so X(t) = (0.01cm/sec)(t sec) + 3.6 cm, or, omitting units,

X(t) = 0.01t + 3.6

= the length parameter after t seconds, in cm.


V(X) = 2X^3 cm^3

= the volume when the length parameter is X.


dV(X(t))/dt = (dV(X)/dX)(X(t)) × dX(t)/dt

that is, (V ∘ X)'(t) = V'(X(t)) × X'(t) chain rule


V'(X) = 6X^2 cm^3/cm

= the rate of change of volume per change in length parameter when the length parameter is X, units cm^3/cm. Not a constant (why?).


X'(t) = 0.01 cm/sec

= the rate of change of length parameter per change in time parameter, after t seconds, units cm/sec.

V(X(t)) = (V ∘ X)(t) = 2(0.01t+3.6)^3 cm^3

= the volume after t seconds, in cm^3

V'(X(t)) = 6(0.01t+3.6)^2 cm^2

= the rate of change of volume per change in length parameter, after t seconds, in units cm^3/cm.

(V ∘ X)'(t) = ( 6(0.01t+3.6)^2 cm^3/cm )(0.01 cm/sec) = 0.06(0.01t+3.6)^2 cm^3/sec

= the rate of change of the volume per change in time, in cm^3/sec, after t seconds.


Problem to ponder: why is (V ∘ X)'(t) not a constant? Does the change in volume of a cube per change in side length depend on the side length?


Question part b)


Given y=2x²+3x, use differentiation to find small change in y when x increased from 4 to 4.02.


This is a little ambiguous, but "use differentiation" suggests that we want y'(4.02) yunit per xunit, rather than Δy/Δx = (y(4.02)-y(4))/(0.02).


Neither of those make much sense, so I think we are to estimate Δy given x and Δx, without evaluating y(x) at all.

Then we want y'(x+Δx/2)×Δx


y(x) = 2x^2 + 3x

y'(x) = 4x + 3


y(4) = 44

y(4.02) = 44.3808

Δy = 0.3808

Δy/Δx = (0.3808)/(0.02) = 19.04


y'(4) = 19

y'(4.01) = 19.04

y'(4.02) = 19.08


Estimate Δy = (y(x+Δx)-y(x)/Δx without evaluating y() at all, using only y'(x), given x = 4, Δx = 0.02.


y'(x+Δx/2)×Δx = y'(4.01)×0.02 = 19.04×0.02 = 0.3808.


In this case, where y is quadratic in x, this method gives Δy exactly.

6 0
3 years ago
To conserve water, many communities have developed water restrictions. The water utility charges a fee of $38, plus an additiona
earnstyle [38]

Using a linear function, the correct option regarding the situation is given by:

C) 57 ≤ 1.28x + 38 ≤ 87; To stay within the range, the usage should be between 14.8 and 38.3 HCF.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The bill is modeled by a linear function, with an <u>intercept of $38 and a slope of $1.28</u>, hence it is given by:

C(x) = 1.28x + 38

The bill should be between $57 and $87 dollars per month, hence:

57 <= C(x) <= 87.

The values of x are:

C(x) >= 57

1.28x + 38 >= 57

x >= 19/1.28

x >= 14.8.

C(x) >= 87

1.28x + 38 >= 87

x >= 49/1.28

x >= 38.3.

Hence option C is correct.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

8 0
2 years ago
Determine if the statement is always, sometimes or never true.
Romashka-Z-Leto [24]

Let

x--------> the measure of the adjacent interior angle

y--------> the measure of an exterior angle at the vertex of a polygon

we know that

The measure of the adjacent interior angle and the measure of an exterior angle at the vertex of a polygon are supplementary angles

so

x+y=180°

<u>Examples</u>

case 1)

<u>In a square</u>

x=90°

so

y=180-90=90°

x=y

In this case

The measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle

case 2)

<u>an equilateral triangle</u>

x=60°

so

y=180-60=120°

x\neq y

In this case

The measure of an exterior angle at the vertex of a polygon is not equals the measure of the adjacent interior angle

therefore

<u>the answer is</u>

sometimes



4 0
3 years ago
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