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3 years ago

Could somebody please answer these four questions with simple yet explanatory answers?

Mathematics

2 answers:

Olin [163]3 years ago

8 0

Pooja answered #1 and #2 correct, so I shall make my life easier by answering #3 and #4 :P

#3 tests the concept of surface area. The gift wrap will be covering only the surface of each side. Surface area is all of the outside. Volume is all of the stuff inside.

So the surface area of rectangular prism can be found by the formula:
SA = 2(LW + LH + WH)
SA = 2(9*7 + 7*4 + 9*4)
SA = 2(63 + 28 + 36)
SA = 2(<span>127)
SA = 254 in</span>²<span>

#4 also needs you to find the surface area.
So the surface area of a triangular prism can be found by this formula:
</span>SA = bh + ( $\sf s_1 + s_2 + s_3$ )h
SA = (6.3*2) + (6.3 + 2.5 + 5.2)3
SA = 12.6 + (14*3)
SA = 12.6 + 42
SA = 54.6 cm²

Kamila [148]3 years ago

7 0

1) Surface Area = 2(lw + lh + wh)
2(4*5+4*9+5*9) =202in^2
Surface Area=202in^2
Lateral Area= Perimeter of base * height
5+5=10 <--width+width
4+4=8 <---length + length
10+8=18 <--total perimeter
18 * 9=162in^2 <--multiplied the height +perimeter of base
Lateral Area=162in^2

2) Same concept as the previous one
Surface Area = 2(lw + lh + wh)
2(4*2+4*5+5*2) =76in^2
Surface Area= 76in^2

Lateral Area
Lateral Area= Perimeter of base * height
4+4=8
2+2=4
8+4=12
12 x 5=60
Lateral Area= 60in^2

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Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = e−4x, [0, 2] Yes, it does not m

Zigmanuir [339]

Answer:

(a) Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem.

(b) $c =0.51995$

Step-by-step explanation:

Given

$f(x) = e^{-4x};\ [0,2]$

Solving (a); Does the function satisfy M.V.T on the given interval

We have:

$f(x) = e^{-4x};\ [0,2]$

The above function is an exponential function, and it is differentiable and continuous everywhere

Solving (b): The value of c

To do this, we use:

$f'(c) = \frac{f(b) - f(a)}{b - a}$

In this case:

$[a,b] = [0,2]$

So, we have:

$f'(c) = \frac{f(2) - f(0)}{2 - 0}$

$f'(c) = \frac{f(2) - f(0)}{2}$

Calculate f(2) and f(0)

$f(x) = e^{-4x}$

So:

$f(2) = e^{-4*2} = e^{-8} = 0.00033546262$

$f(0) = e^{-4*0} = e^{0} = 1$

This gives:

$f'(c) = \frac{0.00033546262 - 1}{2}$

$f'(c) = \frac{-0.99966453738}{2}$

$f'(c) = -0.4998$

Note that:

$f'(x) = (e^{-4x})'$

$f'(x) = -4e^{-4x}$

This implies that:

$f'(c) = -4e^{-4c}$

So, we have:

$f'(c) = -0.4998$

$-4e^{-4c} =-0.4998$

Divide both sides by -4

$e^{-4c} =\frac{-0.4998}{-4}$

$e^{-4c} =0.12495$

Take natural logarithm of both sides

$\ln(e^{-4c}) =\ln(0.12495)$

$\ln(e^{-4c}) =-2.0798$

Apply law of natural logarithm

$\ln(e^{ax}) =ax$

So:

$-4c =-2.0798$

Solve for c

$c =\frac{-2.0798}{-4}$

$c =0.51995$

3 0

2 years ago

Which measurement would be least likely to be written in scientific notation

trapecia [35]

The thickness in a dogs hair because depending on how skinny it is. it isn't going to be able to be measured in anything else. it would make the most sense

7 0

2 years ago

What os the slope of a line that is perpendicular to the line shown

Dmitriy789 [7]

Perpendicular lines have slopes that are negative reciprocals.

so first you must find the slope of the line given
the slope formula is

m=(y₂-y₁)/(x₂-x₁)

now you just plug in the coordinate points that you are given

m=(-2-2)/(0-(-3)
m=-4/3

so the slope of the line given is -4/3, the negative reciprocal of this would be 3/4

The slope of the perpendicular line would be 3/4

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2 years ago

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Snowcat [4.5K]

The 3 digits in the unit period is 817

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3 years ago

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Fofino [41]

Answer: a(n)= a(n-1)+5

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