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2 years ago

At what point does the graph of y=9x(x is exponent) cross the y-axis?

Mathematics

1 answer:

uysha [10]2 years ago

3 0

Answer:

-The graph crosses the y-axis at the point (0,0)

None of the given options is correct

A graph crosses the y-axis at the point (0,y).This means that the graph will cross the y-axis when x-=0

To find the point where the graph crosses the y-axis,substitute x=0 into the given equation y-9x

substitute x=0 into the equation y-9x to find the corresponding value of y

That is,

y=9(0)

y=0

therefore the graph crosses the y-axis at the point (0,0)

Step-by-step explanation:

hope it hlps

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Chase's birthday party costs $8 for every guest he invites. How many guests can there be

QveST [7]

Answer:

4 guests

Step-by-step explanation:

If it's $8 every person, 4 x $8 is $32, so he can have 4 guests.

7 0

3 years ago

Read 2 more answers

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.

Otrada [13]

I guess the "5" is supposed to represent the integral sign?

$I=\displaystyle\int_1^4\ln t\,\mathrm dt$

With $n=10$ subintervals, we split up the domain of integration as

[1, 13/10], [13/10, 8/5], [8/5, 19/10], ... , [37/10, 4]

For each rule, it will help to have a sequence that determines the end points of each subinterval. This is easily, since they form arithmetic sequences. Left endpoints are generated according to

$\ell_i=1+\dfrac{3(i-1)}{10}$

and right endpoints are given by

$r_i=1+\dfrac{3i}{10}$

where $1\le i\le10$ .

a. For the trapezoidal rule, we approximate the area under the curve over each subinterval with the area of a trapezoid with "height" equal to the length of each subinterval, $\dfrac{4-1}{10}=\dfrac3{10}$ , and "bases" equal to the values of $\ln t$ at both endpoints of each subinterval. The area of the trapezoid over the $i$ -th subinterval is

$\dfrac{\ln\ell_i+\ln r_i}2\dfrac3{10}=\dfrac3{20}\ln(ell_ir_i)$

Then the integral is approximately

$I\approx\displaystyle\sum_{i=1}^{10}\frac3{20}\ln(\ell_ir_i)\approx\boxed{2.540}$

b. For the midpoint rule, we take the rectangle over each subinterval with base length equal to the length of each subinterval and height equal to the value of $\ln t$ at the average of the subinterval's endpoints, $\dfrac{\ell_i+r_i}2$ . The area of the rectangle over the $i$ -th subinterval is then

$\ln\left(\dfrac{\ell_i+r_i}2\right)\dfrac3{10}$

so the integral is approximately

$I\approx\displaystyle\sum_{i=1}^{10}\frac3{10}\ln\left(\dfrac{\ell_i+r_i}2\right)\approx\boxed{2.548}$

c. For Simpson's rule, we find a quadratic interpolation of $\ln t$ over each subinterval given by

$P(t_i)=\ln\ell_i\dfrac{(t-m_i)(t-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+\ln m_i\dfrac{(t-\ell_i)(t-r_i)}{(m_i-\ell_i)(m_i-r_i)}+\ln r_i\dfrac{(t-\ell_i)(t-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

where $m_i$ is the midpoint of the $i$ -th subinterval,

$m_i=\dfrac{\ell_i+r_i}2$

Then the integral $I$ is equal to the sum of the integrals of each interpolation over the corresponding $i$ -th subinterval.

$I\approx\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}P(t_i)\,\mathrm dt$

It's easy to show that

$\displaystyle\int_{\ell_i}^{r_i}P(t_i)\,\mathrm dt=\frac{r_i-\ell_i}6(\ln\ell_i+4\ln m_i+\ln r_i)$

so that the value of the overall integral is approximately

$I\approx\displaystyle\sum_{i=1}^{10}\frac{r_i-\ell_i}6(\ln\ell_i+4\ln m_i+\ln r_i)\approx\boxed{2.545}$

4 0

3 years ago

Joan works on commission for a furniture store. She gets a base pay of $85 a day plus 6 percent of the

podryga [215]

Answer:

Correct expression: 85 + 0.06(t - 400)

Correct earnings: $91

Step-by-step explanation:

The expression Joan wrote is incorrect because instead, $85, she put $400 as her base salary. The correct expression would be 85 + 0.06(t - 400), where 85 is her base pay in dollars, and t - 400 represents her sales in dollars exceeding $400.

If Joan's sales were $500, she would not make $424.90, but

85 + 0.06(t - 400)

85 + 0.06(500 - 400)

85 + 0.06(100)

85 + 6

$91

Hope this helps.

Cheers,

Andy

7 0

3 years ago

Can someone help me fill in the proofs and statements?

Yuri [45]

Answer:

3. they are both equvilent.

4. onl makes a right angle and mnl makes an upside down right angle.

5.makes a definition.

Step-by-step explanation:

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3 years ago

2x-y<-3

timama [110]

Answer:

y > 2x + 3

Step-by-step explanation:

Okay, first let's simplify the equation by understanding the form.

y = mx + b is the form.

Currently we have 2x - y < -3, So we can subtract 2x on both sides to get

-y < -2x - 3

Let's multiply each term by -1 to get

y < 2x + 3, but wait! We have to flip the sign!

The answer is :

y > 2x + 3

5 0

3 years ago