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3 years ago

A cube has a surface area of 150 square inches (in)

Mathematics

1 answer:

Marta_Voda [28]3 years ago

3 0

Answer:

25in²

Step-by-step explanation:

a cube has 6 faces

all of these are equal

therefore you need to divided 150 by 6

that's 25

the answer is 25 in²

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Solve x^2-y^2+x+1+2yx+y=0

Harlamova29_29 [7]

Combine like terms and use inverse operations

4 0

3 years ago

Please help me if you can

IRISSAK [1]

Answer:

8π in

64π mm²

Step-by-step explanation:

The circumference of a circle is equal to 2πr, where r is the radius.

2π(4) = 8π ≈ 25.132

The area of a circle is equal to πr²

π(8)² = 64π ≈ 201.062

8 0

3 years ago

If x + 2 is a factor of x^2 +mx + 14 find m

jolli1 [7]

X² + mx + 14

If (x+2) one of the factors, we can write

14 = 2*7
m = 2+7= 9

x² +9x + 14 = (x+2)(x+7)

3 0

3 years ago

What is the inverse of the function?<br> f(x) = 1/3x-5

OlgaM077 [116]

Answer:

-1

f (x) = -3(x + 5)

Step-by-step explanation:

1) in f(x) = 1/3x-5, replace f(x)= with y= as follows: y = (1/3)x - 5

2) interchange x and y, obtaining: x = (1/3)y - 5

3) solve this result for y: (1/3)y = -x - 5, or -(x + 5). Next, multiply both sides by 3 to eliminate the fraction (1/3): y = -3(x + 5)

4) replace y with the symbol for "inverse of f(x);

-1

f (x) = -3(x + 5)

5 0

3 years ago

g Use this to find the equation of the tangent line to the parabola y = 2 x 2 − 7 x + 6 at the point ( 4 , 10 ) . The equation o

natali 33 [55]

Answer:

The tangent line to the given curve at the given point is $y=9x-26$ .

Step-by-step explanation:

To find the slope of the tangent line we to compute the derivative of $y=2x^2-7x+6$ and then evaluate it for $x=4$ .

$(y=2x^2-7x+6)'$ Differentiate the equation.

$(y)'=(2x^2-7x+6)'$ Differentiate both sides.

$y'=(2x^2)'-(7x)'+(6)'$ Sum/Difference rule applied: $(f(x)\pmg(x))'=f'(x)\pm g'(x)$

$y'=2(x^2)'-7(x)'+(6)'$ Constant multiple rule applied: $(cf)'=c(f)'$

$y'2(2x)-7(1)+(6)'$ Applied power rule: $(x^n)'=nx^{n-1}$

$y'=4x-7+0$ Simplifying and apply constant rule: $(c)'=0$

$y'=4x-7$ Simplify.

Evaluate y' for x=4:

$y'=4(4)-7$

$y'=16-7$

$y'=9$ is the slope of the tangent line.

Point slope form of a line is:

$y-y_1=m(x-x_1)$

where $m$ is the slope and $(x_1,y_1)$ is a point on the line.

Insert 9 for $m$ and (4,10) for $(x_1,y_1)$ :

$y-10=9(x-4)$

The intended form is $y=mx+b$ which means we are going need to distribute and solve for $y$ .

Distribute:

$y-10=9x-36$

Add 10 on both sides:

$y=9x-26$

The tangent line to the given curve at the given point is $y=9x-26$ .

------------Formal Definition of Derivative----------------

The following limit will give us the derivative of the function $f(x)=2x^2-7x+6$ at $x=4$ (the slope of the tangent line at $x=4$ ):

$\lim_{x \rightarrow 4}\frac{f(x)-f(4)}{x-4}$

$\lim_{x \rightarrow 4}\frac{2x^2-7x+6-10}{x-4}$ We are given f(4)=10.

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

Let's see if we can factor the top so we can cancel a pair of common factors from top and bottom to get rid of the x-4 on bottom:

$2x^2-7x-4=(x-4)(2x+1)$

Let's check this with FOIL:

First: $x(2x)=2x^2$

Outer: $x(1)=x$

Inner: $(-4)(2x)=-8x$

Last: $-4(1)=-4$

---------------------------------Add!

$2x^2-7x-4$

So the numerator and the denominator do contain a common factor.

This means we have this so far in the simplifying of the above limit:

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

$\lim_{x \rightarrow 4}\frac{(x-4)(2x+1)}{x-4}$

$\lim_{x \rightarrow 4}(2x+1)$

Now we get to replace x with 4 since we have no division by 0 to worry about:

2(4)+1=8+1=9.

6 0

3 years ago