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3 years ago

PLZ HELP I ONLY HAVE A FEW MINS LEFT

Mathematics

2 answers:

Sholpan [36]3 years ago

7 0

Answer:

The area is 10 square units

Step-by-step explanation:

A = 1/2bh

A = 1/2(4)(5)

A = 10 square units

Hope this is accurate & helpful!

egoroff_w [7]3 years ago

5 0

10 square units is the answer

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At 4:00p.m the temperature was 90F after this point the temperature dropped 1.5F per hour until sunrise the next morning write a

irina [24]

Answer:

90t-21t=69t

Step-by-step explanation:

4:00pm to 6:00 am is 14 hours. 14 x 1.5 is in fact 21 which means the temperature dropped 21 degrees in those 14 hours.

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3 years ago

Prime factorization of 1050

Shkiper50 [21]

The Prime Factorization of 1050: 2*3*5^2*7<span />

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3 years ago

can someone help me?, I had the notes in my notebook but the notebook got full, so I threw it away not thinking I was gonna need

Natalija [7]

Step-by-step explanation:

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3 years ago

The students in Mr. Wilson's Physics class are making golf ball catapults. The

Mnenie [13.5K]

Answer:

Part a) About 48.6 feet

Part b) About 8.3 feet

Part c) The domain is $0 \leq x \leq 48.6\ ft$ and the range is $0 \leq y \leq 8.3\ ft$

Step-by-step explanation:

we have

$y=-0.014x^{2} +0.68x$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

where

x is the ball's distance from the catapult in feet

y is the flight of the balls in feet

Part a) How far did the ball fly?

Find the x-intercepts or the roots of the quadratic equation

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-0.014x^{2} +0.68x=0$

$a=-0.014\\b=0.68\\c=0$

substitute in the formula

$x=\frac{-0.68(+/-)\sqrt{0.68^{2}-4(-0.014)(0)}} {2(-0.014)}$

$x=\frac{-0.68(+/-)0.68} {(-0.028)}$

$x=\frac{-0.68(+)0.68} {(-0.028)}=0$

$x=\frac{-0.68(-)0.68} {(-0.028)}=48.6\ ft$

therefore

The ball flew about 48.6 feet

Part b) How high above the ground did the ball fly?

Find the maximum (vertex)

$y=-0.014x^{2} +0.68x$

Find out the derivative and equate to zero

$0=-0.028x +0.68$

Solve for x

$0.028x=0.68$

$x=24.3$

<em>Alternative method</em>

To determine the x-coordinate of the vertex, find out the midpoint between the x-intercepts

$x=(0+48.6)/2=24.3\ ft$

To determine the y-coordinate of the vertex substitute the value of x in the quadratic equation and solve for y

$y=-0.014(24.3)^{2} +0.68(24.3)$

$y=8.3\ ft$

the vertex is the point (24.3,8.3)

therefore

The ball flew above the ground about 8.3 feet

Part c) What is a reasonable domain and range for this function?

we know that

A reasonable domain is the distance between the two x-intercepts

$0 \leq x \leq 48.6\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 48.6 feet

A reasonable range is all real numbers greater than or equal to zero and less than or equal to the y-coordinate of the vertex

we have the interval -----> [0,8.3]

$0 \leq y \leq 8.3\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 8.3 feet

8 0

2 years ago

Evaluate the expression.

Katarina [22]

Answer:

Step-by-step explanation:

The lines on the outside simply means "absolute value". This just takes any negative number and makes it positive. In this case, 15-4 is already positive so the answer is just positive 11.

4 0

2 years ago